Discrete Jacobian-Pseudoinverse-Free Zhang Neurodynamics Algorithm Handling Path Tracking of Robot Manipulator With Unknown Model

Abstract

Robot manipulator path tracking, recognized as a crucial aspect in robot manipulator control, has garnered significant attention from researchers. In this paper, to address the path tracking problem of robot manipulators with unknown models, a novel Jacobian pseudoinverse estimator is first proposed based on Zhang neurodynamics method. The estimator directly provides an efficient and accurate estimation of the Jacobian matrix pseudoinverse, avoiding the complicated operation of matrix pseudoinverse and preventing potential singularity phenomenon of the Jacobian matrix. By utilizing the Euler difference formulas, a discrete model-free and Jacobian-pseudoinverse-free Zhang neurodynamics algorithm is proposed. The proposed algorithm focuses on leveraging the available current and previous known information to predict the future unknown information. Detailed theoretical analyses and proofs ensure the convergence and stability of the proposed algorithm. Finally, comparative experiments with various effective model-free algorithms, and experimental validations on different types of robot manipulators (UR5, Franka Emika Panda, and Kinova Gen3 robot manipulators) using various experimental platforms (MATLAB, CoppeliaSim, and physical platforms) illustrate the effectiveness of the proposed algorithm. Note to Practitioners—This paper is motivated by addressing the prevalent challenge of unknown models in real-time path tracking for robot manipulators. In this paper, a novel discrete model-free and Jacobian-pseudoinverse-free Zhang neurodynamics algorithm is proposed. Different from the existing model-free algorithms, the proposed algorithm avoids the complicated operation of computing the pseudoinverse of matrix without compromising precision, significantly reducing the computational complexity and preventing potential singularity phenomenon of the Jacobian matrix. The average computation time per updating for the proposed algorithm is approximately $0.1\,{\mathrm { ms}}$ , which is significantly less than the sampling gap of the operation. This allows it to effectively meet the real-time requirements for robot manipulator path tracking. In addition, the error of the proposed algorithm is approximately $2\,\mu {\mathrm { m}}$ , which can meet the requirements of most practical application scenarios. Moreover, the accuracy of the algorithm is limited by the differential formula and sampling gap. Improving the accuracy and robustness of the algorithm by using more accurate difference formulas and filtering technique will be our future research direction.